In wavelength division multiplexed (WDM) optical communication systems, a number of different optical carrier wavelengths are separately modulated with data to produce modulated optical signals. The modulated optical signals are combined into an aggregate signal and transmitted over an optical transmission path to a receiver. The receiver detects and demodulates the data.
One type of modulation that may be used in optical communication systems is phase shift keying (PSK). According to different variations of PSK, data is transmitted by modulating the phase of an optical wavelength such that the phase or phase transition of the optical wavelength represents symbols encoding one or more bits. In a binary phase-shift keying (BPSK) modulation scheme, for example, two phases may be used to represent 1 bit per symbol. In a quadrature phase-shift keying (QPSK) modulation scheme, four phases may be used to encode 2 bits per symbol. Other phase shift keying formats include differential phase shift keying (DPSK) formats and variations of PSK and DPSK formats, such as return-to-zero DPSK (RZ-DPSK) and polarization division multiplexed QPSK (PDM-QPSK).
A modulation format, such as QPSK wherein multiple information bits are to be encoded on a single transmitted symbol may be generally referred to as a multi-level modulation format. Multi-level modulation techniques have been used, for example, to allow increased transmission rates and decreased channel spacing, thereby increasing the spectral efficiency (SE) of each channel in a WDM system. One spectrally efficient multi-level modulation format is quadrature amplitude modulation (QAM). In a QAM signal, information is modulated using a combination of phase shift keying and amplitude shift keying, for example, to encode multiple bits per symbol. An M2-QAM signal may be used to encode M bits per symbol. For example, a 16-QAM modulation format may be used to encode 4 bits per symbol. PSK modulation schemes (e.g., BPSK and QPSK) may be referred to as a level of QAM (e.g., 2 QAM and 4 QAM respectively).
Higher order QAM schemes are useful in realizing flexi-rate transponder technology wherein multiple data rates may be achieved over the same bandwidth (or symbol rate) using different SE. Multiple SEs can be realized using QAM by varying the amount of redundancy in the design, e.g. higher redundancy leads to a lower SE. The redundancy can come from altering the overhead (OH) of the forward error correction code (FEC) used in the scheme, or by introducing a simple extra layer of coding that is mainly used for coded modulation purposes. Coded modulation is particularly useful when the symbol rate, constellation grid and FEC overhead are fixed.
In phase modulated optical communication systems using, for example, a QAM scheme, the receiver may be a coherent receiver using coherent detection, e.g. homodyne or heterodyne detection, to detect modulated optical signals. The term “coherent” when used herein in relation to a receiver refers to a receiver including a local oscillator (LO) for demodulating the received signal. Digital signal processing (DSP) may be implemented in such systems for processing the received signals to provide demodulated data. Digital signal processing of the received signal provides speed and flexibility, and may be used to perform a variety of functions including correction of nonlinearities associated with the optical transmission path such as chromatic dispersion, polarization mode dispersion, etc.
Coherent detection schemes for phase modulated systems may use absolute phase detection. Absolute phase detection may involve making a decision, e.g. a soft decision, regarding the value of each bit in the received data stream based on an estimated phase. Unfortunately, for M2-QAM, e.g., QPSK and 16 QAM, the signal constellation is invariant under a phase rotation of angle π/2. The carrier phase estimator used to determine the estimated phase cannot distinguish between an angle θ and an angle θ+π/2. As a result, the estimated carrier phase may be pushed away from the current stable operating point into the domain of attraction of a neighboring stable operating point, which effectively rotates the signal constellation by π/2. This phenomenon is referred to as cycle slip. The cycle slip can generate a large number of decision errors after the cycle slip event. The effect of cycle slip can be limited to the duration of actual slip by using differential decoding of the information symbols. However, the differential decoding can have about twice the bit error rate of the absolute phase detection.
One approach for correcting cycle slip is to introduce pilot symbols with known information symbols. The pilot symbols remove the phase ambiguity since the carrier phase of the pilot symbol can be unambiguously estimated by calculating the difference of the phase between the received pilot symbol and the known information symbols. However, the overhead of the pilot symbol causes a larger symbol rate resulting in a sensitivity penalty. To address this, pilot symbols may be inserted with a large period. In general, it may take about half the number of symbols between pilot symbols period before the cycle slip is detected and the carrier phase reference is corrected. The time it takes to make the correction can result in burst errors in the detected data.